It is a strange little phrase but in its immediate context—
4 The Lord is in his holy temple;
the Lord's throne is in heaven;
his eyes see, his eyelids test the children of man.
5 The Lord tests the righteous,
but his soul hates the wicked and the one who loves violence.
6 Let him rain coals on the wicked;
fire and sulfur and a scorching wind shall be the portion of their cup.
7 For the Lord is righteous;
he loves righteous deeds;
the upright shall behold his face.
—it does tend to suggest that God can look directly at us and judge even when his eyes are closed.
A comfort for the righteous who think that God has forgotten them, and a terror for the wicked.
I'm blogging Psalm 11 over at the Sola Panel, and there is another post from the other day about a mission statement for church.